One of the key features of neapolitan dough is a healthy amount of elasticity. This is required to be able to drag a fully loaded pizza to the peel.

I find that my dough never has that elasticity. It can just support pulling over a Margherita to the peel. But if I add a few more ingredients or leave it on the board for as long as a minute, the dough becomes infinitely extensible but with no elasticity. There's no way I can do the Da Michele oblong stretch. If I try it, only the edges where I'm pulling would stretch, the rest of the pizza would be fixed to the (bamboo) board.

Here's how I make my dough. I don't have a mixer so I always mix/knead by hand/spoon. I mix most of it in the wet stage per Varasano then gradually add flour until it's done. Total mix/knead time is around 15min. 63% hydration. 2.2% salt. 2% culture. I will add in rest periods as needed to help with absorption. Toward the end I do flap/fold or letter folds as needed to make the dough smooth and incorporate air. I ball pretty tight following Da Michele's method of pushing dough toward a central point and pinching/rolling around that.

I ferment in balls between 12-48 hours at 58F in my wine fridge. My containers are slightly on the tall side so the dough doesn't fully flatten out as in a tray. I open the dough balls when they're inflated by about 50%. Even with modest inflation, I find once I flatten out the dough, there are lots of moderate sized bubbles. I use Ischia starter with no added yeast.

I am very gentle when I open up my dough. I don't firmly press into the disk with my fingers as in some videos. I gently pat it (never loud) until it's 8" and then I do a few over the knuckle rotations. Often the center gets paper thin (the first sign of trouble) but I've been trying to avoid that.

After initial topping I can stretch it to the peel but any added time or ingredient and it's pretty much stuck. It's not just lack of bench flour. The dough itself feels like it has no elasticity.

Lastly, despite using no more than 2% of culture, my dough tastes moderately sour. Not over sour, but definitely not mild. I always get the feeling sugars are being depleted.

Should I be shaping/pressing it more aggressively when I open the ball? Is something wrong in the mixing stage? Is my culture not working at peak and eating up all the sugars?

Make sure you only make one change at a time and make notes of the outcome. For me the notes are crucial because I bake pizzas only a couple times a month and I tend to forget what the outcome really was.

If you haven't already done it I personally would dial down your hydration to about 60%. That would be an easy first thing to try.

Still using Ischia and it seems to be working better. I now dunk the dough ball into a flour bowl. I used to just lightly sprinkle the dough ball with flour. Gentle handling/flattening seems to be the key to balancing elasticity and extensibility. I still would like to see more elasticity but now the dough seems strong enough to handle a bit more time/weight.